Page 35 - Color Atlas Physiology

!
The higher the k value, the more quickly the sub- (! p. 176 ff.). Since the pH of a solution deter-
stance will diffuse through a pure phospholipid mines whether these substances will be
bilayer membrane. Substitution into Eq. 1.3 gives charged or not (pK value; ! p. 378), the diffu-
∆C sion of weak acids and bases is clearly depend-
–1
J diff ! k ! A ! D ! [mol ! s ]; [1.4]
∆x ent on the pH.
The previous equations have not made al-
Whereas the molecular radius r (! Eq. 1.1) still lowances for the diffusion of electrically
largely determines the magnitude of D when k re- charged particles (ions). In their case, the elec-
mains constant (cf. diethylmalonamide with ethyl- trical potential difference at cell membranes
Fundamentals and Cell Physiology of the membrane. –1 [1.5] diffusion (electrodiffusion). In that case, posi-
urea in D), k can vary by many powers of ten when r
must also be taken into account. The electrical
remains constant (cf. urea with ethanol in D) and can
potential difference can be a driving force of
therefore have a decisive effect on the permeability
tively charged ions (cations) will then migrate
Since the value of the variables k, D, and ∆x
to the negatively charged side of the mem-
within the body generally cannot be deter-
brane, and negatively charged ions (anions)
mined, they are usually summarized as the
will migrate to the positively charged side. The
permeability coefficient P, where
prerequisite for this type of transport is, of
D
course, that the membrane contain ion chan-
P ! k !
[m ! s ].
nels (! p. 32 ff.) that make it permeable to the
∆x
–1
along a concentration gradient carries a charge
area A, Eq. 1.4 is transformed to yield
and thus creates an electric diffusion potential
1 If the diffusion rate, J diff [mol!s ], is related to transported ions. Inversely, every ion diffusing
J diff ! P ! ∆C [mol ! m –2 ! s ]. [1.6] (! p. 32 ff.).
–1
A
As a result of the electrical charge of an ion, the per-
The quantity of substance (net) diffused per meability coefficient of the ion x (= P x) can be trans-
unit area and time is therefore proportional to formed into the electrical conductance of the
∆C and P (! E, blue line with slope P). membrane for this ion, g x (! p. 32):
When considering the diffusion of gases, ∆C 2 2 –1 –1 –2
in Eq. 1.4 is replaced by α· ∆P (solubility coeffi- g x ! ! P x ! z x ! F R ! T ! c x [S ! m ] [1.9]
cient times partial pressure . difference; where R and T have their usual meaning (explained
3
–1
–1
! p. 126) and J diff [mol ! s ] by V diff [m ! s ]. above) and z x equals the charge of the ion, F equals
–1
4
k · α · D is then summarized as diffusion con- the Faraday constant (9,65 ! 10 A ! s ! mol ), and c x
equals the mean ionic activity in the membrane.
ductance, or Krogh’s diffusion coefficient K [m ! Furthermore,
2
s ! Pa ]. Substitution into Fick’s first diffusion
–1
–1
equation yields c ! c 1 –c 2 . [1.10]
. lnc 1 –lnc 2
V diff ! K ! ∆P [m ! s ]. [1.7]
–1
A ∆x where index 1 = one side and index 2 = the other side
of the membrane. Unlike P, g is concentration-depend-
Since A and ∆x of alveolar gas exchange ent. If, for example, the extracellular K concentration
+
(! p. 120) cannot be determined in living or- rises from 4 to 8 mmol/kg H 2O (cytosolic concentra-
ganisms, K · F/∆x for O 2 is often expressed as tion remains constant at 160 mmol/kg H 2O), c will
the O 2 diffusion capacity of the lung, D L: rise, and g will increase by 20%.
. Since most of the biologically important
V O 2diff ! D L ! ∆P O 2 [m ! s ]. [1.8]
3
–1
substances are so polar or lipophobic (small
Nonionic diffusion occurs when the uncharged k value) that simple diffusion of the substances
form of a weak base (e.g., ammonia = NH 3) or through the membrane would proceed much
acid (e.g., formic acid, HCOOH) passes through too slowly, other membrane transport proteins
a membrane more readily than the charged called carriers or transporters exist in addition
form (! F). In this case, the membrane would to ion channels. Carriers bind the target
22 be more permeable to NH 3 than to NH 4 + molecule (e.g., glucose) on one side of the
membrane and detach from it on the other side
Despopoulos, Color Atlas of Physiology © 2003 Thieme
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